Solve for $x$ and $y$ using elimination. ${-4x-y = -34}$ ${-5x+y = -29}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-9x = -63$ $\dfrac{-9x}{{-9}} = \dfrac{-63}{{-9}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-4x-y = -34}\thinspace$ to find $y$ ${-4}{(7)}{ - y = -34}$ $-28-y = -34$ $-28{+28} - y = -34{+28}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {-5x+y = -29}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + y = -29}$ ${y = 6}$